Extension of Noncommutative Soliton Hierarchies

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dc.creatorDimakis, Aristophanes
dc.creatorMuller-Hoissen, Folkert
dc.date2004-01-21
dc.date2004-03-05
dc.date.accessioned2026-07-07T10:49:49Z
dc.date.available2026-07-07T10:49:49Z
dc.descriptionA linear system, which generates a Moyal-deformed two-dimensional soliton equation as integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The supplementary integrability conditions result in a first order differential equation with respect to the deformation parameter, the flow of which commutes with the flow of the deformed soliton equation. In this way, a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations. We prove the extended hierarchy properties for the deformed AKNS hierarchy, and specialize to the cases of deformed NLS, KdV and mKdV hierarchies. Corresponding results are also obtained for the deformed KP hierarchy. A deformation equation determines a kind of Seiberg-Witten map from classical solutions to solutions of the respective `noncommutative' deformed equation.
dc.description19 pages, some minor changes in section 4, typos in (2.4),(3.38),(4.15) corrected, to appear in Journal of Physics A
dc.identifierhttps://arxiv.org/abs/hep-th/0401142
dc.identifierhttp://arxiv.org/abs/hep-th/0401142
dc.identifierJ.Phys.A37:4069-4084,2004
dc.identifierdoi:10.1088/0305-4470/37/13/010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184347
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleExtension of Noncommutative Soliton Hierarchies
dc.typetext

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